## Learn More about Ratios and Proportions

Dietary research is often conducted with an aim to examine one variable in relation to another. [glossary term:] Ratios, including proportions, are useful devices for addressing such relationships. Ratios can be used to depict the value of one variable divided by the value of another. A proportion, often expressed as a percentage, is a kind of ratio that can be used to represent the value of a single variable for one class divided by the value for all classes combined. A common proportion used in dietary research is the amount of a food or nutrient per 1000 kilocalories.

Two types of ratios are commonly used and conceptualized in dietary research: the mean ratio and the ratio of means. The mean ratio is calculated by determining the ratio for each person (or each day) and then taking a mean of the ratios.

a/b + a/b + a/b

3

The ratio of means is calculated by summing the numerator variable for all persons (or each day) and dividing by the sum of the denominator variable.

a + a + a

b + b + b

Because the result would be the same if the summed numerator and denominator each were divided by a constantâ€”such as the number of persons in the population (or days of intake), which would result in a mean value for both the numerator and denominatorâ€”this is called a ratio of means.

(a + a + a)/3

(b + b + b)/3

It is important to note that the mean ratio and the ratio of means (also called the population ratio) can be different. This is true whether the subjects of interest are individuals in the population or separate days of intake (reported using a short-term instrument). Because of this possible discrepancy, it is important to keep in mind how these two types of ratios are calculated and that they are not measuring exactly the same thing.

The ratio of means is generally the preferred method of estimating the ratio of one dietary variable to another for a population.

### For More Information

Freedman LS, Guenther PM, Dodd KW, Krebs-Smith SM, Midthune D.
The population distribution of ratios of usual intakes of dietary components that are consumed every day can be estimated from repeated 24-hour recalls.
*J Nutr* 2010 Jan;140(1):111-6.
[View Abstract]

Freedman LS, Guenther PM, Krebs-Smith SM, Kott PS.
A population's mean Healthy Eating Index-2005 scores are best estimated by the score of the population ratio when one 24-hour recall is available.
*J Nutr* 2008 Sep;138(9):1725-9.
[View Abstract]

Krebs-Smith SM, Kott PS, Guenther PM.
Mean proportion and population proportion: two answers to the same question?
*J Am Diet Assoc* 1989 May;89(5):671-6.
[View Abstract]